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CRC PUBLICATIONS |
A Technique to Interpolate Frequency Curves between Frequent Events and Probable Maximum Events
Lionel Siriwardena
Erwin Weinmann
Publication Type:
Technical Report
This is a publication of the initial CRC for Catchment Hydrology
CRC Program:
Flood Hydrology (Previous CRC)
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Publication Keywords:
Rainfall/Runoff Relationship
Frequency Analysis
Precipitation (Atmospheric)
Design Data
Flood Forecasting
Statistical Analysis
Methods
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Abstract / Summary:
This report describes a pragmatic approach to extend directly derived rainfall frequency curves to the probable maximum precipitation (PMP) through a well defined transition function. Importantly, the slope of the interpolated curve is not constrained in approaching the PMP, unlike in the present Australian Rainfall and Runoff (ARR87) procedure.
The 'generalised procedure' to fill the 'gap' in the frequency curve was developed on the basis of work by Lowing (1995) for the UK; a simple 2-parameter parabolic function was fitted in log-log space to satisfy requirements at either end of the curve. Conditions for satisfactory behaviour of the function were stipulated. The report presents two specific adaptations of the generalised procedure; ie (i) to extend the frequency curve from an AEP of 1 in 2000 to the PMP, to apply with CRC-FORGE based design rainfall frequency curves and (ii) to extend the frequency curve from an AEP of 1 in 100 to the PMP, with design rainfall quantiles estimated from the ARR87 procedures.
The proposed interpolation procedure has been shown to perform satisfactorily over a large range of theoretical conditions and design situations:
- different starting points for interpolation (AEP of 1 to 100 to 1 in 2000);
- different AEPs assigned to the PMP (ranging from 10-4 to 10-7 depending on the catchment size);
- different 'shape parameters' defined by the ratio of the slope of the upper end of the directly determined frequency growth curve, Sgc, and the slope between the two end points of the 'gap', Sgap, (the 'shape parameters' Sgc/Sgap ranging from 0.25 to 2.0).
For satisfactory application of the procedure in practical design situations, the directly determined part of the frequency curve and the PMP with its assigned AEP must be compatible. This conditions places upper and lower limits on the acceptable shape parameter values. The application of the procedure can be extended to interpolate flood frequency curves; compatibility checks are particularly important when applying it directly to design floods, generally estimated to a lower AEP limit of 1 in 100.
Application of the new methodology to 25 Victorian catchments of diverse characteristics showed that the resultant rainfall frequency curves were plausible and well behaved; the new interpolation procedure can be successfully applied for diverse practical design situations. The methodology was also found to be satisfactory in application to shorter storm durations (<24 hours), with design rainfalls for AEPs 1 in 200 to 1 in 2000 estimated by an approximate procedure; frequency curves were shown to be consistent over a practically significant range of storm durations.
Limited testing on rainfall frequency curves for Victorian catchments indicated that the new interpolation procedure resulted in a significant reduction of the design estimates in the interpolated range compared to those derived from the current interpolation procedure (Chapter 13, ARR87).
The proposed interpolation procedure is of purely empirical nature. While it is able to bridge significant gaps, the uncertainty of the interpolated values is expected to increase with the size of the gap. This uncertainty should be kept in mind when basing decisions on interpolated rainfall or flood data.
This report is not currently available for downloading. Printed copies are available from the Centre Office
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Centre Office:
CRC for Catchment Hydrology
Dept of Civil Engineering
Building 60
Monash University Vic 3800
Tel: +61 3 9905 2704
Fax: +61 3 9905 5033
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